Question

Find the constants a and b such that the function is continuous on the entire line

f(x){7, x is less than or equal to -3
ax+b, -3 is less than x is greater than 4
-7, x is less than or equal to 4

Answer 1

you need a smooth transition from (-3,7) to (4,-7)

y-7 = -14/7 (x+3)
or
y = -2x + 1

so, a=-2, b=1